Hooke's law (contd...)

Furthermore, the stress strain relations must remain unaltered when the axes are rotated to a new position. Say x and y axes are rotated about the z axes through angle to a new location and . Then the relation , from equations 2.18b and 1.29 results in

which results in , and the expression for and in equation 26 simplifies to,

(3.14)

Historically, and were substituted as

which resulted in the following expressions for the stresses in terms of the strains,

(3.15)

The constants, and are called the Lame's constants.